What does the argmax of the expectation of the log likelihood mean?
This equation and more information of it can be found in Expectation Maximization Wikipedia site and the explanation there was as follows (formula there in two parts):



Some more explanation from same page:


  In statistics, an expectation–maximization (EM) algorithm is an iterative method to find maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step.


Mathematically, E in your equation stands for Expectation Value,  x|theta is conditional probability and x~data and model are sub-titles of source of probability in either case. The arg max theta is argument theta that maximizes the equation.